A note on the ε entropy of monotone functions in the levy norm

The ? entropy of the class $\text{F1}$ of real-valued monotone functions from [0, 1] to [0, 1] in the usual Chebyshev norm is infinite, due to the discontinuities in some of the $\text{f ? F1}$. One of the class of norms introduced by P. Lévy for analyzing the convergence of distribution functions gives finite ? entropy $\text{～(}\text{1}\text{?}\text{)}$. (There is an obvious extension to the class $\text{F1}{}_{\mathrm{AB}}$ of monotone functions from [0, A] to [0, B].